I think the question is "if the original is destroyed, would you step into the transporter?"
Ok. If that's the question, then why not? Your sequence of memories is the same. Nobody has found evidence of a single unit called 'self' in the mind. It's an illusion produced by the sequence of memories formed up until a certain point. Therefore, the object with those memories would be standing on the other side, recalling the apprehension it felt before stepping in, and would be glad that it did so as it is now existing in another place (as intended) with a retained sense of self.
I do not understand what this means.
Sorry. I was trying to describe what I meant by it being a matter of definition.
The word same has slightly different denotations, depending on the context. If you walk into a shop and see a man buy a newspaper, and you approach the shop keeper and say 'I'll have the same paper, thanks', he's not going to run after the other guy and snatch the paper off him to sell to you. Likewise, if you hired a squash racket one week, and ask the counter assistant for a racket the following week and say 'I'll have the same one I used last week', they'll most likely give you the exact same racket, understand that you don't want one that is the same make and brand, but want that actual same racket.
The term can be blurred when one asks if a person who is replicated is the same person. The definition needs to be very precise.
I do not see why it is necessary for you to say that it is only if there is continued existence that they can be said to be different. You have already differentiated between the copy and the original. If you had not then you might be able to say that on their continued existence there becomes two different individuals, but I do not see how you could say of these individuals that one is the "I".
I'm not. I'm saying it depends on the definitions.
In the respect of these bodies being the thing which athon thinks is athon, are they the same?
Again, it depends on the definition of same. Each will identify with the self called Athon, but it depends on what the term same means as to whether the copy is the same as the original.
Athon